Related papers: Rigorous Continuum Limit for the Discrete Network …
Motivated by an application to resource sharing network modelling, we consider a problem of greedy maximization (i.e., maximization of the consecutive minima) of a vector in $R^n$, with the admissible set indexed by the time parameter. The…
We study a generic family of nonlinear dynamics on undirected networks generalising linear consensus. We find a compact expression for its equilibrium points in terms of the topology of the network and classify their stability using the…
This paper extends the definitions of effective resistance and effective conductance to characterize the overall relation (positive coupling or antagonism) between any two disjoint sets of nodes in a signed graph. It generalizes the…
Discrete dynamic models are a powerful tool for the understanding and modeling of large biological networks. Although a lot of progress has been made in developing analysis tools for these models, there is still a need to find approaches…
Optimal transport (OT) theory provides a principled framework for modeling mass movement in applications such as mobility, logistics, and economics. Classical formulations, however, generally ignore capacity limits that are intrinsic in…
The outstanding problem of controlling complex networks is relevant to many areas of science and engineering, and has the potential to generate technological breakthroughs as well. We address the physically important issue of the energy…
There are several applications in computational biophysics which require the optimization of discrete interacting states; e.g., amino acid titration states, ligand oxidation states, or discrete rotamer angles. Such optimization can be very…
Robustness of routing policies for networks is a central problem which is gaining increased attention with a growing awareness to safeguard critical infrastructure networks against natural and man-induced disruptions. Routing under limited…
We prove a Quantitative Functional Central Limit Theorem for one-hidden-layer neural networks with generic activation function. The rates of convergence that we establish depend heavily on the smoothness of the activation function, and they…
For a finite point set $E\subset \mathbb{R}^d$ and a connected graph $G$ on $k+1$ vertices, we define a $G$-framework to be a collection of $k + 1$ points in E such that the distance between a pair of points is specified if the…
In this paper, we investigate the linear controllability framework for complex networks from a physical point of view. There are three main results. (1) If one applies control signals as determined from the structural controllability…
In this paper we consider complex dynamical networks modeled by means of state space systems running in discrete time. We assume that the dependency structure of the variables within the (nonlinear) network equations is known and use…
We derive a dimension-reduction limit for a three-dimensional rod with material voids by means of $\Gamma$-convergence. Hereby, we generalize the results of the purely elastic setting [57] to a framework of free discontinuity problems. The…
The control of complex networks has generated a lot of interest in a variety of fields from traffic management to neural systems. A commonly used metric to compare two particular control strategies that accomplish the same task is the…
We analyse the rigidity of discrete energies where at least nearest and next-to-nearest neighbour interactions are taken into account. Our purpose is to show that interactions beyond nearest neighbours have the role of penalising changes of…
We consider in-network computation of an arbitrary function over an arbitrary communication network. A network with capacity constraints on the links is given. Some nodes in the network generate data, e.g., like sensor nodes in a sensor…
We obtain several sharp spectral bounds, approximations, and exact values for the isoperimetric number and related edge-expansion parameters of graphs. Our results focus on graph powers and on families of graphs with rich algebraic or…
In this note, we study Laplacians on graphs for which connectivity within certain subgraphs tends to infinity. Our main focus are graphs sharing a common node set on which edge weights within certain clusters grow to infinity. As…
This paper initiates a limit theory of permutation valued processes, building on the recent theory of permutons. We apply this to study the asymptotic behaviour of random sorting networks. We prove that the Archimedean path, the conjectured…
We consider the inverse problem for countable, locally finite electrical networks with edge weights in an arbitrary field. The electrical inverse problem seeks to determine the weights of the edges knowing only the potential and current…